Master` Equation for the Penrose-Diosi wavefunction collapse

In summary, the conversation discusses equation 209 on page 81 of the arXiv paper, which concerns the master equation for Penrose-Diosi collapse. The equation describes a system in a superposition of two distinct particle configurations and includes terms for Schrodinger evolution and objective collapse. The term [tau-d(X,X')] represents the average time for a collapse to occur and is calculated in terms of gravitational energy. The conversation also raises questions about the meaning of certain terms and symbols in the equation.
  • #1
Agrippa
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TL;DR Summary
Hope you'll help me understand specific aspects of the equation better
I'm trying to understand equation 209 on page 81 here: https://arxiv.org/pdf/1204.4325.pdf

Here's what I understand so far:
- We are to imagine a system in a superposition of |X> and |X'>, where these describe distinct particle configurations.
- On the RHS of the eqn, the first term is Schoredinger evolution, the second term represents effects of objective collapse.
- The term [tau-d(X, X')] gives a number, which represents the average time for a collapse of this superposition to occur. This is calculated in terms of the gravitational energy required to create system S1 in |X> and system S2 in |X'> starting with S1 and S2 both being in state |X>.

Here's what I don't yet understand?
- What is the exact meaning of the LHS term, in particular, what does it mean to sandwich the density operator of the system between the two eigenstates of the superposition like this?
- Why does the first rho on the RHS of the eqn not have a hat on it, whereas the other two rhos do?
- Why do we take [tau-d(X, X')] to the power of -1?
- What is the physical significance of the two subtraction signs? e.g. what happens if the first is deleted, or the second is changed to addition?

Hope you can help! :-)
 
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p.s. this thread concerns the master equation for Penrose-Diosi collapse (as opposed to, for example, the state vector evolution equation for Penrose-Diosi collapse). It is PhysForum editors that keep changing the title from "Master equation for..." to the slightly less sexy "Mastering this equation for..."
 
  • #3
Moderator's note: Thread title restored.
 
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Likes Agrippa and berkeman

1. What is the Master Equation for the Penrose-Diosi wavefunction collapse?

The Master Equation for the Penrose-Diosi wavefunction collapse is a mathematical equation that describes the process by which the wavefunction of a quantum system collapses into a definite state. It was proposed by physicists Roger Penrose and Lajos Diosi as a way to explain the collapse of the wavefunction in the objective reduction (OR) theory of consciousness.

2. How does the Master Equation work?

The Master Equation takes into account the interaction between the quantum system and its environment. It describes how the wavefunction of the system evolves over time and how it is affected by the environment. When the system interacts with the environment, it undergoes a series of collapses until it reaches a definite state.

3. What is the significance of the Master Equation in quantum mechanics?

The Master Equation is significant because it offers a possible explanation for the collapse of the wavefunction in quantum mechanics. It also provides a connection between quantum mechanics and consciousness, as the OR theory suggests that consciousness plays a role in the collapse of the wavefunction.

4. Are there any criticisms of the Master Equation?

Yes, there are some criticisms of the Master Equation. Some scientists argue that it is not a complete or accurate description of the wavefunction collapse and that it relies too heavily on the role of consciousness. Others argue that it is not testable or falsifiable, making it more of a philosophical concept than a scientific theory.

5. Is the Master Equation widely accepted in the scientific community?

The Master Equation is still a topic of debate and research in the scientific community. While it has gained some support from physicists and philosophers, it is not widely accepted as a complete explanation for the wavefunction collapse. Further research and experimentation are needed to fully understand the role of the Master Equation in quantum mechanics.

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